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Introducing Spatial Element in ODE Model for Cell-Mediated Immune Response to Tumor Growth

Author: Giorgi Gachechiladze
Co-authors: Giorgi Gabunia, Keti Gomiashvili, Keti Kakhidze
Keywords: Mathematical Modelling, Ordinal Differential Equations, Partial Differential Equations, Diffusion, Immune Response, Tumor Growth, Parallel Computing, Numerical Simulations

Our goal was to extend functionality of Phillis's ODE mathematical model about the immune response to tumor growth. We assumed that cell movement can be described with diffusion equations; in that way we added spatial element to Phillis’s onedimensional ODE model and transformed it to Partial Differential Equations with diffusion. We created numerical scheme for our model and impemented on computer using C++ programming language and three different parallelisation mechanisms.

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